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Plug-in hybrid electric vehicles (PHEVs) will be widely used in future transportation systems to reduce oil fuel consumption. Therefore, the electrical energy demand will be increased due to the charging of a large number of vehicles. Without intelligent control strategies, the charging process can easily overload the electricity grid at peak hours. In this paper, we consider a smart charging and discharging process for multiple PHEVs in a building's garage to optimize the energy consumption profile of the building. We formulate a centralized optimization problem in which the building controller or planner aims to minimize the square Euclidean distance between the instantaneous energy demand and the average demand of the building by controlling the charging and discharging schedules of PHEVs (or ‘users’). The PHEVs' batteries will be charged during low-demand periods and discharged during high-demand …